MILWAUKEE -- LeBron James recalls that July jackpot moment back in Las Vegas like it was yesterday.

James wasn't at any of the tables or slot machines. Instead, he was in a basketball gym hosting a summer tournament that showcased 100 of the nation's top prep prospects.

When his cell phone rang, James stepped aside for a moment to take the call informing him that Ray Allen had agreed to leave the Boston Celtics to sign with the Miami Heat. James hung up the phone and called Allen right away.

“The first thing I said was, 'This is what we've been talking about for a while,'” James said Thursday as he reflected on that moment in free agency with Allen last summer. “I've always tried to be in his ears, saying, 'Hey, let's join at some point. Let's join. Let's join.' And he was like, 'The time is now.' I knew what he was able to do against me in the past. I knew that threat could add another dimension to our team we haven't had our first two years in Miami.”

It's no wonder James celebrated the hardest Thursday night when Allen reached another career milestone late in the Heat's 104-91 win to take a commanding 3-0 series lead against Milwaukee in the first round of the playoffs.

Allen's 3-pointer with 8:38 left in the game moved him past Reggie Miller to become the NBA's career leader for made 3s in the playoffs. It also capped a devastating 23-7 run that gave the Heat their largest lead at 17 points.

Allen finished with a team-high 23 points, two short of matching the Heat's all-time record for scoring by a reserve in a postseason game. Allen was 5-of-8 from beyond the arc to bring his career playoff total to 322 made 3-pointers. Allen had already passed Miller to become the league's career leader in total 3-point field goals made overall.

Thursday's moment for Allen carried additional sentimental value because it came in the Bradley Center, where he spent the first six years of his career with the Bucks.

“I just think about all the guys that came before me,” Allen said of the shooters he learned from earlier in his career. “There's so many great players, great shooters that have set the bar. Reggie set the bar. Craig Hodges, I looked up to. I played with Dale Ellis and Dell Curry, both of those guys and Ricky Pierce. I got to see first-hand what it took to prepare and what it took to be a great shooter at any moment in the game. I'm just carrying on the torch.”

On Thursday, that torch was aimed at the Bucks. And the Heat needed every bit of the extra spark Allen provided on a night when Dwyane Wade had the worst playoff shooting performance of his career and Chris Bosh struggled early.

Wade missed 11 of his 12 shots and had six turnovers, but also contributed 11 assists, nine rebounds, five steals and two blocks. Wade's four points were the second-fewest of his career in a playoff game, and he said after the game that he was dealing with recurring soreness in his right knee. Wade also missed most of the second half to receive treatment on the bench for a bruised right forearm.

In many ways, it was Ray Appreciation Day for the Heat.

Wade thanked Allen in the locker room for “picking me up” and carrying the scoring lead at shooting guard.

“We don't take him for granted,” Heat coach Eric Spoelstra said of Allen, who has played in Boston, Seattle and Milwaukee during his 17-year career. “He's Everyday Ray. Having someone of his caliber, with his resume, off the bench is significant. Without him, we probably don't have a chance to pull away in the fourth. He's done this everywhere he's been. We've been on the other end. That's why we recruited him so hard. He knocks down two, three or four to put you away.”

And that has been a demoralizing reality for the Bucks, who continued a trend of matching the Heat's energy and effort well into the second half, only to see Miami put the game out of reach with a game-changing spurt down the stretch.

Miami used a 9-0 charge in Game 1 on the way to a 110-87 victory. In Game 2, the Heat went on a 12-0 to start the fourth quarter with James anchoring a group of reserves that included Allen, Shane Battier, Norris Cole and Chris Andersen. That unit also inflicted the damage Thursday and have the Heat within a victory Sunday of completing their first series sweep since James arrived three seasons ago.

Jennings essentially said the Bucks can only contain so many of the Heat's weapons. With Wade and Bosh struggling and James held largely in check, the Bucks built a 10-point lead in the first half and felt good about their chances of rallying to get back into the series.

But then Allen warmed up on those familiar rims.

“Ray Allen played here for a long time in his career, so he's used to this arena,” Jennings said. “That was one of the turning points right there. He was knocking down a lot of 3s and getting into the paint. He was really being aggressive. When you have another guy like that coming off the bench, it brings a spark. They are a tough team to beat with LeBron, [Wade] and Bosh. Ray comes in and contributes, and that is what really caused us problems.”

In many ways, Allen is just starting to get comfortable in his role with the Heat. After being a starter throughout his career, Allen struggled to find his rhythm and role at times during his first season as a full-time reserve in Miami. He was also still dealing with recovery soreness in his ankle after having surgery last summer to remove bone spurs.

But Allen appears to have found his footing in his first playoff series with the Heat. He has scored at least 20 points in two of the three games against Milwaukee and is averaging 16.6 points, 3.3 rebounds, and 3 assists while shooting 42.8 percent from 3-point range in the series.

“In the playoffs there are so many things that take place,” Allen said. “You just have to hunker down and find a way to make this team better. Now we [face] the same team. I know who my matchup is, the plays they're running and what we need to run to be successful. I try to find every opportunity, every moment to be more efficient out on the floor, to make these guys better and allow them to make me better. It's easier more now to settle in.”

Allen was once a player that beat the Heat with big shots.

Now he's providing them a significant postseason boost.

“The No. 1 thing when I got an opportunity to talk to him is it seemed like he had a new start and a breath of fresh air,” James said of that initial discussion with Allen last summer. “It's continued ever since that conversation.”